The energy effects of cycles and pairs of cycles in mono- and dicyclopenta-derivatives of anthracene and phenanthrene are computed by a graph-theoretical method. Our results show that there is no significant difference between the extent of cyclic conjugation in anthracene and its cyclopenta-derivative (aceanthrylene) and phenanthrene and its cyclopenta-derivative (acephenanthrylene). In contrast to this, the presence of two cyclopentane rings causes drastic changes in the modes of cyclic conjugation. Our results provide an explanation for the peculiar stability order: dicyclopenta[de,mn] anthracene (never isolated) < dicyclopenta[de,kl]anthracene (stable) 1000oC).